Electric Potential A difference in electrical potential between the upper atmosphere and the ground can cause electrical discharge (motion of charge).

Ch 25 – Electric Potential So far, we’ve discussed electric force and fields. Now, we associate a potential energy function with electric force. This is identical to what we did with gravity last semester. gravity electricity ?

Ch 25.1 – Electric Potential and Potential Difference Place a test charge, q0, into an E-field. The charge will experience a force: This force is a conservative force. Pretend an external agent does work to move the charge through the E-field. The work done by the external agent equals at least the negative of the work done by the E-field.

Do Now (9/19/13): What does the word “voltage” mean to you? Where have you seen the word before? What is the formula for work? (think back to last year!)

Ch 25.1 – Electric Potential and Potential Difference Potential difference due to work being done on a particle This physical quantity only depends on the electric field. Potential Difference – the change in potential energy per unit charge between two points in an electric field. Units: Volts, [V] = [J/C] A change in electric potential energy can only occur if a test charge actually moves through the E-field.

Ch 25.1 – Electric Potential and Potential Difference Units of the potential difference are Volts: 1 J of work must be done to move 1 C of charge through a potential difference of 1 V.

Ch 25.1 – Electric Potential and Potential Difference We now redefine the units of the electric field in terms of volts. E-field units in terms of volts per meter

Voltage What is the formula for work? Simplify:

Example: What is the voltage on a proton at rest in an E-field of 20 N/C?

Practice: Complete AT LEAST one problem from the Potential Difference paper When you finish, raise your hand to get it stamped Once you have your stamp you may work on that paper, your quiz review, or your notecard

Ch 25.1 – Electric Potential and Potential Difference Another useful unit (in atomic physics) is the electron-volt. One electron-volt is the energy required to move one electron worth of charge through a potential difference of 1 volt. If a 1 volt potential difference accelerates an electron, the electron acquires 1 electron-volt worth of kinetic energy. The electron-volt

Quick Quiz 25.1 Points A and B are located in a region where there is an electric field. How would you describe the potential difference between A and B? Is it negative, positive or zero? Pretend you move a negative charge from A to B. How does the potential energy of the system change? Is it negative, positive or zero?

Ch 25.2 – Potential Difference in a Uniform E-Field Let’s calculate the potential difference between A and B separated by a distance d. Assume the E-field is uniform, and the path, s, between A and B is parallel to the field.

Ch 25.2 – Potential Difference in a Uniform E-Field Let’s calculate the potential difference between A and B separated by a distance d. Assume the E-field is uniform, and the displacement, s, between A and B is parallel to the field. 1

Ch 25.2 – Potential Difference in a Uniform E-Field The negative sign tells you the potential at B is lower than the potential at A. VB < VA Electric field lines always point in the direction of decreasing electric potential.

Ch 25.2 – Potential Difference in a Uniform E-Field Now, pretend a charge q0 moves from A to B. The change in the charge-field PE is: If q0 is a positive charge, then ΔU is negative. When a positive charge moves down field, the charge-field system loses potential energy.

Ch 25.2 – Potential Difference in a Uniform E-Field Electric fields accelerate charges… that’s what they do. What we’re saying here is that as the E-field accelerates a positive charge, the charge-field system picks up kinetic energy. At the same time, the charge-field system loses an equal amount of potential energy. Why? Because in an isolated system without friction, mechanical energy must always be conserved.

Ch 25.2 – Potential Difference in a Uniform E-Field If q0 is negative then ΔU is positive as it moves from A to B. When a negative charge moves down field, the charge-field system gains potential energy. If a negative charge is released from rest in an electric field, it will accelerate against the field.

Ch 25.2 – Potential Difference in a Uniform E-Field Consider a more general case. Assume the E-field is uniform, but the path, s, between A and B is not parallel to the field.

Ch 25.2 – Potential Difference in a Uniform E-Field Consider a more general case. Assume the E-field is uniform, but the path, s, between A and B is not parallel to the field.

Ch 25.2 – Potential Difference in a Uniform E-Field If s is perpendicular to E (path C-B), the electric potential does not change. Any surface oriented perpendicular to the electric field is thus called a surface of equipotential, or an equipotential surface.

Quick Quiz 25.2 The labeled points are on a series of equipotential surfaces associated with an electric field. Rank (from greatest to least) the work done by the electric field on a positive charge that moves from A to B, from B to C, from C to D, and from D to E.

EG 25.1 – E-field between to plates of charge A battery has a specified potential difference ΔV between its terminals and establishes that potential difference between conductors attached to the terminals. This is what batteries do. A 12-V battery is connected between two plates as shown. The separation distance is d = 0.30 cm, and we assume the E-field between the plates is uniform. Find the magnitude of the E-field between the plates.

EG 25.1 – Proton in a Uniform E-field A proton is released from rest at A in a uniform E-field of magnitude 8.0 x 104 V/m. The proton displaces through 0.50 m to point B, in the same direction as the E-field. Find the speed of the proton after completing the 0.50 m displacement.